When constituting an optical system, there is such case that only a light with a specified wavelength is output to perform optical treatment. An optical device capable of outputting the light of bandwidth including a specified wavelength is referred to as a wavelength filter. The wavelength filter can be produced by evaporating a thin film material with a high refractive index and a thin film material with a low refractive index on a substrate of glass or plastic. The wavelength or bandwidth can be adjusted by altering the number of evaporation and thickness of the thin film. In order to enhance the wavelength selectivity, however, the number of evaporation and/or thickness of the thin film are required to be increased. Accordingly, the production process becomes complicated to push up the cost and, since the constitution becomes complicated, the suppression of variation of performance becomes difficult.
Recently, such wavelength filter is proposed that has a simpler construction and a sharp wavelength selectivity, the wavelength filter being produced by forming a diffraction grating having a microscopic periodic structure on a substrate surface, and depositing a high refractive index medium thereon. The wavelength filter has such characteristic that can reflect only a very narrow wavelength band of several nanometers or less, while utilizing the localization (confinement) and scattering effects of light in a periodic structure referred to as a resonance phenomenon. For example, S. S. Wang and R. Magnusson: “Theory and application of guided-mode resonance filters,” Applied Optics Vol. 32 No. 14 2606-2613 (1993) discloses a wavelength filter having narrow-band reflection spectrum by arranging a grating structure in which a material of low refractive index and a material of high refractive index are alternately arranged in a period shorter than the wavelength.
FIG. 9 is a drawing showing the constitution of the above-described wavelength filter. On the surface of a substrate 701, a diffraction grating that composed of a portion 703 and portion 705 and has a period A shorter than the wavelength λ of light to be used is formed. The portion 703 and portion 705 are composed of materials with different refractive indices. The portion 703 and portion 705 form a layer 707.
When light enters, under a predetermined condition, diffracted lights of +1 order and −1 order is generated, whose waves proceed in a state nearly horizontal to the substrate surface and which can exist only in the layer 707. The wave of light is referred to as an evanescent wave, and the layer 707 is referred to as a waveguide layer. The predetermined condition is represented by the following formula when representing the angle of incident light by θ:
                    [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          1                ]                                                            β        =                                                            2                ⁢                                                                  ⁢                π                            λ                        ⁢            sin            ⁢                                                  ⁢            θ                    +                                    2              ⁢                                                          ⁢              π                        Λ                                              (        1        )            wherein β is a propagation factor. When representing the average refractive index of the waveguide layer 707 by[Mathematical Formula 2] n,β is represented by the formula:
                    [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          3                ]                                                            β        ≈                                            2              ⁢                                                          ⁢              π                        λ                    ⁢                                    n              _                        .                                              (        2        )            
The thickness of the waveguide layer 707 satisfies the following formula:
                    [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          4                ]                                                                                  n            _                    ·          h                =                              λ            2                    .                                    (        3        )            
Here, the formulae (2) and (3) including the average refractive index are approximate ones, and it is necessary to carry out analysis while taking the behavior of electromagnetic wave between the waveguide layer and surrounding layers into consideration in actual analysis.
The evanescent wave that occurred when the formula (1) is satisfied can not transmit when light enters the boundary between the waveguide layer and the neighboring layer, and all the light is subjected to total internal reflection. Therefore, the structure shown in FIG. 9 forms a filter that reflects the light with a very narrow wavelength band determined according to the formula (1).
However, in the reflection characteristic thereof, there is such problem that the reflectivity largely lowers in accordance with a minute wavelength variation and thus an intended half-value width (bandwidth) can not be realized.
In order to solve the problem, D. K. Jacob, S C. Dunn and M. G. Moharam: “Flat-top narrow-band spectral response obtained from cascaded resonant grating reflection filters,” Applied Optics Vol. 41 No. 7 1241-1245 (2002) discloses a wavelength filter in which the wavelength band with the maximum reflectivity is broadened by using materials of 4 types of refractive indices. In the wavelength filter, plural grating structures formed by alternately arranging a material of low refractive index and a material of high refractive index at a predetermined period and thin films with the remaining two types of refractive indices interposed between the plural grating structures are laminated in the incident direction of light.
In addition, S. T. Thurman and G. M. Morris: “Controlling the spectral response in guided-mode resonance filter design,” Applied Optics Vol. 42 No. 16 3225-3233 (2003) discloses a wavelength filter in which a wavelength band with the maximum reflectivity is broadened by similarly laminating grating structures by using only 2 types of materials with a low refractive index and a high refractive index.
In either of the structures described in the documents of D. K. Jacob, S. C. Dunn et al. and S. T. Thurman et al., a broad wavelength band can be obtained by laminating plural grating structures. A broad wavelength band can be obtained because plural wavelengths that bring about the resonance effect are caused to exist, and respective spectra overlap with each other to broaden the wavelength band.
However, in order to produce these structures, the step of producing plural grating structures and the step of evaporating a material of thin film in plural times are required, and the control of the grating structure and thin film height with a high accuracy is required in respective steps. In addition, along with the broadening of the wavelength band, the number of the grating structures to be laminated increases. As the result, as is the case for filters according to conventional thin film techniques, the production process becomes complicated to increase the cost, and the constitution becomes complicated to make it difficult to suppress variation of performance.
Further, since plural grating structures are laminated, the total height (thickness) becomes large.